The Twilio Developer Contest is an ongoing competition that encourages developers to try Twilio for different use cases, industries, and integrations. The contest has been running for over a year and offers various prizes, including a Kindle 3G, $100 in Twilio credit, and other Twilio gear, to reward the winners. Developers can submit their projects and ideas by the deadline of May 29th and get help from the Twilio community through forums or email support. The contest aims to inspire developers from all backgrounds to find success with Twilio and solve problems using its cloud communications platform.